Find the general solutions of sin 2x - sin 4x + sin 6x = 0.

$x = \frac{n π}{4}$

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$x = \frac{n π}{2}$

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$x = n π$

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$x = n π \pm \frac{π}{6}$

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Solution

The correct options are
A
$x = \frac{n π}{4}$

D
$x = n π \pm \frac{π}{6}$

$s i n 2 x - s i n 4 x + s i n 6 x = 0 (s i n 2 x + s i n 6 x) - s i n 4 x = 0 2 s i n 4 x c o s 2 x - s i n 4 x = 0 s i n 4 x (2 c o s 2 x - 1) = 0 s i n 4 x = 0 o r c o s 2 x = \frac{1}{2} 4 x = n π o r 2 x = 2 n π \pm \frac{π}{3} x = \frac{n π}{4} o r x = n π \pm \frac{π}{6}$

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